1. Arithmetic Sequences as Functions

2. Vocabulary
Sequence – an ordered list of numbers that often form a pattern
Term – each number in the sequence

3. Just two more vocab words!
Arithmetic Sequence – this is a pattern in which the difference between consecutive terms is constant
A pattern in which you add or subtract by the same number every time
Common Difference – the constant difference in an arithmetic sequence

4. Describe the pattern in each sequence
5, 8, 11, 14, …
The pattern is to “add 3” to the previous term!
What are the next two terms?
= 17 and = 20
So the next two terms are:
17 and 20

5. Describe the pattern in each sequence
400, 200, 100, 50, …
The pattern is to multiply the previous term by ½
What are the next two terms?
50(1/2) = 25 and 25(1/2) = 12.5
So the next two terms are:
25 and 12.5

6. The common difference is….
Tell whether the sequence is arithmetic. If it is, identify the common difference.
19, 8, -3, -14, …
YES! 
The common difference is….
-11 WHY????

7. Tell whether the sequence is arithmetic
Tell whether the sequence is arithmetic. If it is, identify the common difference.
10, -20, 40, -80 …
No! 

8. Writing Sequences as Functions

11. Arithmetic Sequences as Functions
NEWSPAPERS The arithmetic sequence 12, 23, 34, 45, ... represents the total number of ounces that a bag weighs after each additional newspaper is added.
A. Write a function to represent this sequence.
+11
+11
+11
The common difference is 11.

12. Arithmetic Sequences as Functions
an = a1 + (n – 1)d Formula for the nth term
= (n – 1)11 a1 = 12 and d = 11
= n – 11 Distributive Property
= 11n Simplify.
Answer: The function is an = 11n + 1.

13. SHIPPING The arithmetic sequence 22, 40, 58, 76, … represents the total number of ounces that a box weighs after each additional bottle of salad dressing is added. A. Write a function to represent this sequence.